Dress and Siebeneicher (DS88) generalized the Witt vector construction to the case of pro-$p$ groups for prime integer $p$. These functors, $W_G$, were originally defined for all profinite groups, $G$, and are now called Witt-Burnside functors due to the fact that they generalize both the $p$-typical (recovered when $G = \mathbb{Z}_p$ as an additive group) and ‘big’ Witt vector construction (recovered when $G = \hat{\mathbb{Z}}$), as well as Burnside functors (recovered as $W_G(\mathbb{Z})$).

Witt-Burnside functors have been used to study equivariant ring spectra as they arise as a left adjoint for Tambara functors.

References

A. Dress, C. Siebeneicher, The Burnside ring of profinite groups and the Witt vector construction, Adv. Math., 70, (1988), 87–132.

Lance Edward Miller, On the structure of Witt-Burnside rings attached to pro-p groups, (arXiv:1103.4644)

Last revised on June 10, 2015 at 11:27:34.
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